Ionic Coherence in Resonant Above-Threshold Attosecond Ionization Spectroscopy

The ionization of atoms with sequences of attosecond pulses gives rise to excited ionic states that are entangled with the emitted photoelectron. Still, the ionic ensemble preserves some coherence that can be controlled through the laser parameters. In helium, control of the $2s/2p$ He$^+$ coherence is mediated by the autoionizing states below the $N=2$ threshold [Phys. Rev. Res. {\bf 3}, 023233 (2021)]. In the present work we study the role of the resonances both below and above the $N=3$ threshold on the coherence of the $N=3$ He$^+$ ion, in the attosecond pump-probe ionization of the helium atom, which we simulate using the newstock \emph{ab initio} code. Due to the fine-structure splitting of the N=3 He$^+$ level, the ionic dipole beats on a picosecond timescale. We show how, from the dipole beating, it is possible to reconstruct the polarization of the ion at its inception.